The US moon landings were a hoax, a cure for cancer exists but is being suppressed by drugs companies, vaccinations are harmful, the Earth is actually flat and climate change is a fraud.

Hard to debunk quickly, the adherents of these supposed conspiracies are not difficult to find online. But Dr David Robert Grimes, a physicist and cancer researcher at Oxford University, has come up with a mathematical model to poke holes in them.

The model gives the probability of success for different conspiracies factoring in the number of conspirators, the length of time, the possibility of a leak and even the effects of conspirators dying.

“It is common to dismiss conspiracy theories and their proponents out of hand, but I wanted to take the opposite approach, to see how these conspiracies might be possible,” he said. “To do that, I looked at the vital requirement for a viable conspiracy - secrecy.”

Conspiracy is defined as an effort to explain some event or practice by reference to the machinations of powerful people who attempt to conceal their role (at least until their aims are accomplished).

The rapper Bobby Ray Simmon Jr (aka BoB) unleashed a barrage of tweets this week backing his belief that the Earth is flat, not spherical, and implied that powerful people are trying to conceal the facts.

“here n america, you can be anything, worship anything, & believe anything... EXCEPT the earth not being round... they’ll hang u 4 that 1,” he tweeted.

“they want me to be a “good little rapper” and sing and dance and don’t question things...I’m going up against the greatest liars in history ... you’ve been tremendously deceived.”

Using secrecy as a key criterion of success for a potential conspiracy, Grimes applied his model to four alleged plots, estimating the maximum number of people required to be in on the intrigue, and how long it would take for them to unravel.

Through his equations, Grimes calculated that hoax moon landings (410,000 people) would have been revealed in three years eight months, climate change fraud (405,000 people) in three years and nine months, a coverup of unsafe vaccinations (22,000) in three years and two months and a suppressed cancer cure (714,000 people) in three years and three months.

“My results suggest that any conspiracy with over a few hundred people rapidly collapses, and big science conspiracies would not be sustainable,” he said.

Grimes also looked at the maximum number of people who could take part in a conspiracy in order to maintain it. For a plot to last five years, the maximum was 2,521. For a scheme to remain under wraps for more than a decade, fewer than 1,000 people can be involved. To last a century, a deception should include fewer than 125 collaborators.

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“It made me very interested in how widespread these beliefs are,” he said. “While daft notions on moon landings may be harmless, with climate change it can mean we sleepwalk into damaging inertia.”

Grimes notes a political element in the dismissal of scientific findings. He cites a 2011 study which found conservative white males in the US were far more likely than other Americans to deny climate change.

He acknowledges that some conspiracies were real, from Watergate to the notorious Tuskegee syphilis experiment - when African-American men with the disease were denied access to penicillin - and the recent revelations on data collection by Edward Snowden, the NSA whistleblower. These real conspiracies, however, show that even in highly secretive organisations, there is always a possibility of an accidental or intentional leak whether by whistle-blowing or ineptitude.

“Not every belief in a conspiracy is necessarily wrong - for example, the Snowden revelations confirmed some theories about the activities of the US National Security Agency.”

Grimes argues that conspiracies in scientific domains are particularly hard to sustain, because of scrutiny by fellow scientists: “Even if a small devious cohort of rogue scientists falsified data for climate change or attempted to cover up vaccine information, examination by other scientists would fatally undermine the nascent conspiracy. To circumvent this, the vast majority of scientists in a field would have to mutually conspire - a circumstance the model predicts is exceptionally unlikely to be viable.”

He admits, however, that hard-core conspiracy theorists will not be swayed by his equations: “In these cases, it is highly unlikely that a simple mathematical demonstration of the untenability of their belief will change their viewpoint. However, for the less invested such an intervention might prove useful.”